As we mentioned, the only remaining idealization is the operational verification of O2. Let us suppose that, in an experiment, after doing tomography,We will later discuss the assumption that can one access a tomographically complete set of measurements. one determines that the actual experimental realizations of the ideal preparations are
\(P^{(1)}_a,P^{(1)}_{a^\perp },P^{(1)}_b,P^{(1)}_{b^\perp },P^{(1)}_{aa},P^{(1)}_{{aa}^\perp },P^{(1)}_{bb},P^{(1)}_{{bb}^\perp },P^{(1)}_{\alpha },P^{(1)}_{{\alpha }^\perp }\) , \(P^{(1)}_{\beta }\)  and \(P^{(1)}_{{\beta }^\perp }\) . These 'primary' preparations will, in general, not respect the required operational equivalences in O2, due to unavoidable imperfections in the experimental realisation. Luckily, there are general considerations to tackle this idealization [1]}.
